Aircraft: MEDIUM LARGE TRANSPORT; LOW WING; 2 TURBOJET ENG
Phase of flight: Descent
Anomaly: ATC Issue All Types; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance

An air carrier aircraft was on the GEELA 5 RNAV arrival into Phoenix. The aircraft checked on and the Controller issued him the descend via clearance with runway transition. The aircraft read back the clearance. A few moments later; the Controller issued the aircraft direct GEELA (which is on the RNAV Star) and comply with the speeds starting at GEELA. The aircraft read back the information correctly. The Controller performed a radar handoff approximately 15 miles from the boundary. The aircraft was later shipped to the arrival Controller. I; the FLM; got a phone call from the PHX FLM inquiring why the aircraft was still at 25;000 FT and that the pilot said he never received lower. I went and check the Falcon and Tapes and verified the descent clearance was given correctly and read back by the pilot. Both were indeed done correctly. I spoke to the pilot on the phone and when I told him after reviewing the tapes that he acknowledged the descend via clearance. When I spoke to PHX they asked for control on contact; which we gave. Since PHX gave a descent clearance prior to the GEELA fix; it would cancel the RNAV window restriction over GEELA so technically I don't believe a pilot deviation or airspace deviation occurred. Quite frankly; I believe the pilot either got confused with the descend via clearance or just forgot to enter the execute in the FMS database. After speaking with the Pilot and with the PHX Front Line Manager; I believe all parties agreed a simple mistake was made but corrected. After crossing SCOLE intersection at 25;000 FT and 280k on the GEELA FIVE RNAV arrival to PHX; I left the frequency to listen to the ATIS and prepare for the In Range checklist. When I returned to the frequency a short time later the First Officer briefed me of the changes; ABQ Center had cleared us direct to GEELA intersection and assigned us a speed of 300k or faster until the speed restriction at GEELA. The First Officer then asked me a question regarding the speed restrictions on an RNAV arrival; whether a clearance to comply with a speed at a fix also implied complying with the altitude at that fix. I replied that it did not. I then queried the First Officer whether ATC had not assigned us a 'descend via' clearance. He reiterated that the clearance was for the speed only. We had a brief discussion regarding RNAV arrival procedures and 'descend via' clearances until ABQ Center handed us off to PHX Approach in the vicinity of GEELA intersection. It was apparent that we were quite high on the arrival; PHX Approach kept us informed of their plan for our sequence throughout a series of vectors on the arrival. At no time did ATC indicate that we had missed any clearance restriction or caused any loss of separation. I was confused as to why this had occurred; but assumed it might have something to do with the runway closure in PHX. However; after landing in PHX; I initiated a call to see if there had been a problem on our part. I spoke to an individual there who indicated that we had received and acknowledged a 'descend via' clearance. Neither I nor my First Officer recalls receiving such a clearance. Regardless of where the blame for this incident lies; it is clear to me that I probably could have prevented it. Had I taken the initiative to query ATC one I realized that we were higher than we should normally be at a given point on the arrival. Though the thought did enter my mind; I initially dismissed it assuming that we knew what our clearance was. Contributing to this; I think was my distraction with the In Range checklist. I was busy with 'my' duties and failed to keep situational awareness of the aircraft position on the arrival. An Air Carrier on the GEELA 5 was issued a speed restriction prior to GEELA; but the new First Officer missed the DESCEND VIA clearance and the so the aircraft missed subsequent crossing constraints.